Halftoning is a conversion technique enabling to render continuous tone images or grey scale images on printing devices having a lower tonal resolution. In case of a bi-tonal device, continuous tone information is simulated by controlling the coverage or in other words the amount of pixels in a multi pixel area which are actually rendered as image dots. There is a trade off between spatial resolution and tonal resolution. As a result of the halftoning method, image dots are formed in certain ordered patterns. This may lead to visible artifacts or textures in the printed image. To reduce the appearance of these artifacts the halftoning technique is to be designed to produce patterns that are optimally pleasing for the human eye when printing on a non-ideal printer.
Halftoning techniques can be classified into two main categories: Amplitude Modulated (AM) halftoning and Frequency Modulated (FM) halftoning. In AM halftoning, halftone cells are laid out on a grid with a fixed spatial frequency and angle. The tone is modulated by varying the size of the halftone element (amplitude). In FM halftoning, the halftone element size is constant and may be chosen equal to the size of one pixel but the average distance between the elements (frequency) is varied to produce a certain tone. In contrast to AM halftoning, there are no fixed frequencies or angles.
FM halftoning can be further divided into two subcategories: dithering and error diffusion. FM dithering is characterized by a pixel by pixel comparison of the grey scale images against a dither mask comprising threshold values. The threshold values in the dither mask represent the order in which pixels are turned on for each grey scale level. The dither mask has a predetermined size and is tessellated over the entire image thereby defining a screen such that the grey scale level of each pixel can be compared with a corresponding threshold value of the dither mask enabling to decide whether an image dot is to be printed or not. When halftoning using an error diffusion technique, the grey scale level of each pixel is compared with a corresponding threshold value of the dither mask, however when deciding whether an image dot is to printed or not, the information resulting from comparing neighbouring pixels with their corresponding threshold values is taken into account. Error diffusion techniques are however known to create worm artifacts at low grey scale levels and to require high processing resources.
From all techniques described above, FM dithering seems to be at present the most interesting halftoning technique. FM dithering may however be further divided into stochastic and non-stochastic dithering. In stochastic dithering the threshold values are positioned randomly within the dither mask whereas in non-stochastic dithering the threshold values are positioned in the dither mask in a predetermined order. A potential disadvantage of using non-stochastic dithering masks is that highly structured image dot patterns may be produced which are highly susceptible to positioning errors and hence may introduce banding effects. In stochastic dithering the random or pseudo random positioning of the threshold values in the dither mask is typically based on the global minimization of some spatial or frequency energy function. Examples of stochastic dither masks include the “blue noise masks” as described in U.S. Pat. No. 5,111,310 (Parker et al.), the dither masks generated by the “void and cluster method” as described in U.S. Pat. No. 5,535,020 (Ulichney). A problem associated with the aforementioned examples is that this global stochastic approach for generating dither matrices is complex and time consuming and requires very large processing resources. This problem can be at least partially met by employing the so-called local stochastic dithering technique suggested in “Efficient design of large threshold arrays for accurate tone reproduction”, IS&T's 48th Annual Conference Proceedings, Pages 530-535 by P. Lermant instead of the global stochastic approaches described in U.S. Pat. No. 5,111,310 and U.S. Pat. No. 5,535,020.
When, in order to enable reproduction on a printer, images are halftoned using a screen being based on a global or local stochastic dither mask. In general no direction dependency is taken into account or in other words the stochastic dither mask is generated isotropic. In practice however, the printer may have at least in a printing mode a different print resolution in the print medium propagation direction and a direction perpendicular thereto. For instance, in case the printer is a so-called scanning printer, the printer may have a different printing resolution in the scanning direction and the sub scanning direction, i.e. usually the print medium propagation direction. The fact that stochastic dither masks are not designed to cope with a difference in resolution in both print directions leads to undesired and perceptually disturbing snake-like textures in the printed image in the direction having the higher printer resolution.